Some problems and issues in geophysical turbulence

Velocity fluctuations in the large scales of the atmosphere's meso-scale have turbulent characteristics of random fluctuations and a scale-size distribution near k^−5/3 (Gage, 1979. J. Atmos. Sci. 36, 1950–1954; Lilly, 1983. J. Atmos. Sci. 40, 749–761; Lilly et al., 1998. Theoret. Comput. Fluid Dyn. 11, 139–153). Explanations of this motion field have ranged from inverse cascading quasi-geostrophic (i.e. quasi-two-dimensional) turbulence, to gravity waves (VanZandt, 1982. Geophys. Res. Lett. 9, 575–578). We describe efforts to relate observational spectra to various theories ranging from quasi-geostrophic turbulence to gravity waves. We note that at the larger scales quasi-geostrophic theory may suffice, but at smaller scales, a quasi-geostrophic explanation becomes untenable because the importance of rotation becomes progressively weaker as scales of the flow becomes smaller (the Rossby number approaches unity). We then discuss numerical simulations designed to discriminate between alternative explanations of the flow. Several simulations are reviewed, starting with those of Herring and Métais (1989. J. Fluid Mech. 202, 97–115), and finally those described by Lilly et al. (1998. Theoret. Comput. Fluid Dyn. 11, 139–153).